Learning Objective:
Calculate and understand escape velocity, and visualise the three types of trajectory based on launch speed.
Select Planet
Earth
Moon
Mars
Jupiter
Custom
Mass M (×10²⁴ kg)
5.97
Radius R (×10⁶ m)
6.371
Launch Altitude h above surface (km)
0 km
Escape Velocity
v_esc = √(2GM/R)
11.19 km/s
Minimum speed to escape from surface
v_esc at altitude h
11.19 km/s
v_esc(h) = √(2GM/(R+h))
Energy condition for escape:
Total energy ≥ 0
½mv² - GMm/r ≥ 0 → v ≥ √(2GM/r) = v_esc
Three Trajectories
v < v_esc
7.91 km/s
Elliptical / Falls back
v = v_esc
11.19 km/s
Parabolic / Just escapes
v > v_esc
15.00 km/s
Hyperbolic / Excess velocity
Energy Diagram
Escape Velocity Facts
11.2 km/s
Earth
2.4 km/s
Moon
59.5 km/s
Jupiter